Transcript Lecture 5: Levin & Fox ch.1&2

Sources of Data
Levin and Fox Ch. 1:
•
•
•
•
•
The Experiment
The Survey
Content Analysis
Participant Observation
Secondary Analysis
1
Using numbers to do research
1. Classify, categorize
– Gender, race, religion
2. Rank or Order
– Ideology, policy preferences
3. Score
– Tests, scales
2
Four Levels of Measurement
1. Nominal - offer names for labels for
characteristics (gender, birthplace).
2. Ordinal - variables with attributes we can
logically rank and order.
3
Four Levels of Measurement
3. Interval - distances separating variables
(temperature scale).
4. Ratio - attributes composing a variable are
based on a true zero point (age).
Beware not to treat ordinal measures like
interval (although it is done quite frequently).
4
Uses of Statistics
1. Description
2. Decision-making
– Hypothesis testing
– Should we prescribe this drug (Does this drug
work)?
– Does this policy intervention have an impact?
5
Organizing and Summarizing Data
1.
2.
3.
4.
5.
6.
7.
Frequency distributions
Cumulative distributions
Proportions/Percentages
Ratios and Rates
Percentile Ranks
Cross-tabulations
Graphic presentations
6
Fundamental Concepts of Statistics
Measurement - any result from any procedure that assigns a value to
an observable phenomenon. Problems: our observations are based
on our ability to observe, count, etc. Accuracy is always an issue. It
is virtually impossible to achieve the same measurement twice.
Variation - this brings us to the idea of variation. Statistics is based on
the idea that almost everything varies in someway or has variation.
Two reasons for variation:
1.measurement inaccuracies or error
2. true differences b/w observations, measurement and groups
Error - is always present even when our measures are reliable and
valid since our statistical tests are based on samples.
Probabilistic causation - because of this property we can only deal
with probabilities of being correct or incorrect in our determination
of differences in crime rates.
7
Three Types of Statistics
•
Descriptive - Techniques employed in the presentation of
collected data. Tables, charts, graphs and the formulation of
quantities that indicate concise information about our data.
•
Inferential -Linked with the concept of probability. Statistical
methods that permit us to infer (probabilistically) something
about the real world and about the "true" population from
knowledge derived from only part of that population. Methods
that allow us to specify how likely we will be in error.
•
Predictive- Deals with relationships and the idea that knowing
information about on characteristic or variable can help us
predict the behavior of another variable. Methods and tools
that help predict future observations in other populations or
time periods.
8
Descriptive: Central Tendency
• Mode - The most frequent observation. Usually used with
nominal data to describe data. Limitation - limited information
- could be multi-modal. Cannot be arithmetically manipulated
• Median - the middle observation. Usually used with ordinal
level data. Relatively stable. Limitations - must have ordinal
data or higher. Cannot be arithmetically manipulated
• Mean - Most widely used measure in statistics (i.e., most
statistical tests are built around the mean). Can be
arithmetically manipulated (calculated). Limitations - must
have either interval or ration data, sensitive to outliers
Formula: ∑x / n
9
Let’s play with some data
1. Open up the gss.save data file
– On WebCampus or
– http://faculty.unlv.edu/kfernandez/gss.sav
10
BASIC ALGEGRA CONCEPTS AND NOTATIONS
Definition of Subtraction: a - b = a + (-b)
Multiplicative Inverse: a * (1/a) = 1 (a≠0)
Multiplication times 0: a * 0 = 0
Associative of Multiplication: (a * b) * c = a * (b * c)
Commutative of Multiplication: a * b = b * a
Distributive Law: a(b + c) = ab + ac
Definition of Division: a / b = a(1/b)
11
Polynomial Identities
(a+b)2 = a2 + 2ab + b2
(a+b)(c+d) = ac + ad + bc + bd
a2 - b2 = (a+b)(a-b) (Difference of squares)
(x + a)(x + b) = x2 + ax + bx + ab
ax2 + bx + c = 0 (Quadratic Formula)
12
Powers
xa xb = x (a + b)
xa ya = (xy)a
(xa)b = x (ab)
x(a/b) = bth root of (xa): Example X(1/2) = √X
x(-a) = 1 / xa
x(a - b) = xa / xb
13